The second week of Calculus AB was harder than the first week, although it wasn’t too bad. It really was a continuation of last week’s materials, but we just dug deeper into the information and the problems got harder. In the beginning of the week, we did more advanced product and quotient rule problems. Then, towards the end of the week we learned the derivative rules for arc trig functions.
I understood it for the most part, I just still have some problems with simplifying. Mrs. Robinson practiced a lot with us on it this week, so I don’t think I will too much more trouble with it and it should only get easier. I wasn’t really confused with anything this week because it was just more advanced than last week. So I’ll just explain how to take the derivative of the arc trig functions.
The formula for arccos and arcsin are the same, (1/√1-u^2)(u’). The formulas for arctan and arccot are also the same, (1/1+u^2)(u’), the only difference is that arccot has a negative in front. For example, if you had arctan(3x^2 + 4x) you would plug it into the arctan or tan^-1 formula. (1/1+(3x^2 + 4x)^2 (6x+4). Then you would simplify it. (6x+4/1+9x^4+24x^3+16x^2). These formulas are not hard to understand, it’s just very easy to make simple mistakes. The only thing I’m confused about still is the simplifying, and when to or when not to take the derivative of something while you’re simplifying. I know you are supposed to work from the outside in whenever you are taking derivatives, and that did help me a lot this week. Just need to keep practicing J
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